Khan.scratchpad.disable(); For every level Daniel completes in his favorite game, he earns $680$ points. Daniel already has $430$ points in the game and wants to end up with at least $2200$ points before he goes to bed. What is the minimum number of complete levels that Daniel needs to complete to reach his goal?
Answer: To solve this, let's set up an expression to show how many points Daniel will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Daniel wants to have at least $2200$ points before going to bed, we can set up an inequality. Number of points $\geq 2200$ Levels completed $\times$ Points per level $+$ Starting points $\geq 2200$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 680 + 430 \geq 2200$ $ x \cdot 680 \geq 2200 - 430 $ $ x \cdot 680 \geq 1770 $ $x \geq \dfrac{1770}{680} \approx 2.60$ Since Daniel won't get points unless he completes the entire level, we round $2.60$ up to $3$ Daniel must complete at least 3 levels.